This paper addresses a realistic model for automatic generation control (AGC) design in an interconnected power system. The proposed scheme considers generation rate constraint (GRC), dead band, and time delay imposed to the power system by governor-turbine, filters, thermodynamic process, and communication channels. Simplicity of structure and acceptable response of the well-known integral controller make it attractive for the power system AGC design problem. The Genetic algorithm (GA) is used to compute the decentralized control parameters to achieve an optimum operating point. A 3-control area power system is considered as a test system, and the closed-loop performance is examined in the presence of various constraints scenarios. It is shown that neglecting above physical constraints simultaneously or in part, leads to impractical and invalid results and may affect the system security, reliability and integrity. Taking to account the advantages of GA besides considering a more complete dynamic model provides a flexible and more realistic AGC system in comparison of existing conventional schemes.